Fix equations displaying in benchmarks

docs/src/Salustowicz.md

@@ -5,7 +5,7 @@ The true underlying function HyGP had to approximate is the 1D Salustowicz funct
 
 The Salustowicz benchmark function is as follows:
 
-``f(x) = e^{(-x)} x^3 cos(x) sin(x) (cos(x) sin^2(x) - 1)``
+``f(x) = e^{-x} x^3 \cos(x) \sin(x) (\cos(x) \sin^2(x) - 1)``
 
 Let's import these two packages  `Surrogates` and `Plots`:
 

docs/src/ackley.md

@@ -1,7 +1,7 @@
 # Ackley Function
 
 The Ackley function is defined as:
-``f(x) = -a*exp(-b\sqrt{\frac{1}{d}\sum_{i=1}^d x_i^2}) - exp(\frac{1}{d} \sum_{i=1}^d cos(cx_i)) + a + exp(1)``
+``f(x) = -a*\exp(-b\sqrt{\frac{1}{d}\sum_{i=1}^d x_i^2}) - \exp(\frac{1}{d} \sum_{i=1}^d \cos(cx_i)) + a + \exp(1)``
 Usually the recommended values are: ``a =  20``, ``b = 0.2`` and ``c =  2\pi``
 
 Let's see the 1D case.
@@ -16,15 +16,15 @@ Now, let's define the `Ackley` function:
 
 ```@example ackley
 function ackley(x)
-    a, b, c = 20.0, -0.2, 2.0*π
+    a, b, c = 20.0, 0.2, 2.0*π
     len_recip = inv(length(x))
     sum_sqrs = zero(eltype(x))
     sum_cos = sum_sqrs
     for i in x
         sum_cos += cos(c*i)
         sum_sqrs += i^2
     end
-    return (-a * exp(b * sqrt(len_recip*sum_sqrs)) -
+    return (-a * exp(-b * sqrt(len_recip*sum_sqrs)) -
             exp(len_recip*sum_cos) + a + 2.71)
 end
 ```

docs/src/gramacylee.md

@@ -4,7 +4,7 @@ Gramacy & Lee Function is a continuous function. It is not convex. The function
 ``x \in [-0.5, 2.5]``.
 
 The Gramacy & Lee is as follows:
-``f(x) = \frac{sin(10\pi x)}{2x} + (x-1)^4``.
+``f(x) = \frac{\sin(10\pi x)}{2x} + (x-1)^4``.
 
 Let's import these two packages `Surrogates` and `Plots`:
 

docs/src/tensor_prod.md

@@ -1,6 +1,6 @@
 # Tensor product function
 The tensor product function is defined as:
-``f(x) = \prod_{i=1}^d cos(a\pi x_i)``
+``f(x) = \prod_{i=1}^d \cos(a\pi x_i)``
 
 Let's import Surrogates and Plots:
 ```@example tensor

docs/src/water_flow.md

@@ -1,9 +1,9 @@
 # Water flow function
 
 The water flow function is defined as:
-``f(r_w,r,T_u,H_u,T_l,H_l,L,K_w) = \frac{2*\pi*T_u(H_u - H_l)}{log(\frac{r}{r_w})*[1 + \frac{2LT_u}{log(\frac{r}{r_w})*r_w^2*K_w}+ \frac{T_u}{T_l} ]}``
+``f(r_w,r,T_u,H_u,T_l,H_l,L,K_w) = \frac{2*\pi*T_u(H_u - H_l)}{\log(\frac{r}{r_w})*[1 + \frac{2LT_u}{\log(\frac{r}{r_w})*r_w^2*K_w}+ \frac{T_u}{T_l} ]}``
 
-It has 8 dimension.
+It has 8 dimensions.
 
 ```@example water
 using Surrogates